Practice Dynamic programming with the exercise "2-player game on a calculator"

Learning Opportunities

This puzzle can be solved using the following concepts. Practice using these concepts and improve your skills.

Dynamic programming

Statement

Goal

A number N is displayed on the calculator.

First player picks a digit d between 1 and 9.
N is replaced by N - d.
Second player does the same thing, but has to choose a key which is adjacent to the last one (but not the same one, you cannot repeat the digit select by the opponent).
Repeat until one player gets a negative number. He lost !

For example, we start with N = 20.

7  8  9

4  5  6

1  2  3

First player can pick any digit and hits 8.
N becomes 12.

7  x  9

4  5  6

*  *  *

Second player can pick 4, 5, 6, 7 or 9. He picks 9
N becomes 3.

*  8  x

*  5  6

*  *  *

First player can pick 5, 6 or 8. He picks 5.
N becomes -2.
First player has lost this game.

Your job is to find all winning moves in a starting situation.

Examples:
- if N = 1, then 1 is the only winning move (getting to 0 makes the other player lose since he will have to make N negative on his turn).
- if N = 8, then 5 is NOT a winning move (since second player can reply with 3).

Note: detailed specification of what is "near".

When 1 was selected, then 2, 4 or 5 can be selected.
When 2 was selected, then 1, 3, 4, 5 or 6 can be selected.
When 3 was selected, then 2, 5 or 6 can be selected.
When 4 was selected, then 1, 2, 5, 7, or 8 can be selected.
When 5 was selected, then 1, 2, 3, 4, 6, 7, 8 or 9 can be selected.
When 6 was selected, then 2, 3, 5, 8 or 9 can be selected.
When 7 was selected, then 4, 5 or 8 can be selected.
When 8 was selected, then 4, 5, 6, 7 or 9 can be selected.
When 9 was selected, then 5, 6, or 8 can be selected.

Input

Line 1 : An integer N : the starting number

Output

Line 1 : 0 to 9 integers, separated with spaces, from lowest to highest. These are the winning moves when playing first and N is the starting number

Constraints

0 < N < 1000

Example

Input

Output

1 2

Solve it

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